Rustfmt

I was hoping to implement the image filter/reduction step as well, but that seems to be meaningfully more complex

.gitea/workflows/ci.yml

@@ -1,7 +1,6 @@
 name: "CI"
 on:
   push:
-  pull_request:
   workflow_dispatch:
 
 jobs:
@@ -22,7 +21,10 @@ jobs:
     steps:
       - uses: actions/checkout@v6
       - uses: actions-rust-lang/setup-rust-toolchain@v1
-      - run: cargo check
+        with:
+          components: clippy
+      - run: cargo check --all-targets
+      - run: cargo clippy --all-targets
       - run: cargo test
 
   test-gpu:
@@ -31,5 +33,5 @@ jobs:
     steps:
       - uses: actions/checkout@v6
       - uses: actions-rust-lang/setup-rust-toolchain@v1
-      - run: cargo install --git https://github.com/rust-gpu/rust-gpu cargo-gpu
-      - run: cargo gpu check -p enkou-shaders
+      - run: cargo install --git https://github.com/rust-gpu/rust-gpu cargo-gpu --rev 67f1ff2
+      - run: cargo gpu check --auto-install-rust-toolchain -p enkou-shaders

Cargo.toml

@@ -21,6 +21,10 @@ spirv-std = { git = "https://github.com/Rust-GPU/rust-gpu.git", rev = "67f1ff2"
 
 anyhow = "1.0.102"
 bytemuck = { version = "1.25.0", features = ["derive"] }
-glam = { version = "0.33.1", default-features = false, features = ["libm"] }
+glam = { version = "0.33.1", default-features = false, features = ["bytemuck", "scalar-math"] }
+image = { version = "0.25.10", default-features = false, features = ["default-formats"]}
+libm = "0.2.16"
+rand = { version = "0.10.1", default-features = false }
+rand_xoshiro = "0.8.1"
 rspirv = "0.13.0"
-
+tempfile = "3.27.0"

enkou-shaders-tests/build.rs

@@ -1,5 +1,5 @@
 use cargo_gpu_install::install::Install;
-use cargo_gpu_install::spirv_builder::{ShaderPanicStrategy, SpirvMetadata};
+use cargo_gpu_install::spirv_builder::{Capability, ShaderPanicStrategy, SpirvMetadata};
 use std::path::PathBuf;
 
 pub fn main() -> anyhow::Result<()> {
@@ -9,15 +9,14 @@ pub fn main() -> anyhow::Result<()> {
         .copied()
         .collect::<PathBuf>();
 
-    let mut install = Install::from_shader_crate(crate_path.clone());
-    install.build_script = true;
-    install.auto_install_rust_toolchain = true;
-    let install = install.run()?;
-
+    let install = Install::from_shader_crate(crate_path.clone())
+        .within_build_script()
+        .run()?;
     let mut builder = install.to_spirv_builder(crate_path, "spirv-unknown-vulkan1.3");
     builder.build_script.defaults = true;
     builder.shader_panic_strategy = ShaderPanicStrategy::SilentExit;
     builder.spirv_metadata = SpirvMetadata::Full;
+    builder.capabilities = vec![Capability::Int8, Capability::Int16, Capability::Int64];
 
     let compile_result = builder.build()?;
     let spv_path = compile_result.module.unwrap_single();

enkou-shaders-tests/src/lib.rs

@@ -19,15 +19,12 @@ mod test {
     }
 
     fn has_entry_point(execution_model: ExecutionModel, name: &str) -> bool {
-        for ref entry_point in shader().entry_points.iter() {
+        for entry_point in shader().entry_points.iter() {
             let operands: Vec<Operand> = entry_point
                 .operands
                 .iter()
-                .filter(|op| match op {
-                    Operand::ExecutionModel(_) | Operand::LiteralString(_) => true,
-                    _ => false,
-                })
-                .map(|op| op.clone())
+                .filter(|op| matches!(op, Operand::ExecutionModel(_) | Operand::LiteralString(_)))
+                .cloned()
                 .collect();
 
             assert_eq!(operands.len(), 2);
@@ -56,12 +53,10 @@ mod test {
     }
 
     #[test]
-    pub fn has_entry_main_fs() {
-        assert!(has_entry_point(ExecutionModel::Fragment, "main_fs"))
-    }
-
-    #[test]
-    pub fn has_entry_main_vs() {
-        assert!(has_entry_point(ExecutionModel::Vertex, "main_vs"))
+    fn has_entry_main_camera() {
+        assert!(has_entry_point(
+            ExecutionModel::GLCompute,
+            "main_image_accumulate"
+        ))
     }
 }

enkou-shaders/Cargo.toml

@@ -10,6 +10,14 @@ repository.workspace = true
 workspace = true
 
 [dependencies]
-spirv-std.workspace = true
-glam.workspace = true
 bytemuck.workspace = true
+glam.workspace = true
+libm.workspace = true
+rand.workspace = true
+rand_xoshiro.workspace = true
+spirv-std.workspace = true
+
+[dev-dependencies]
+anyhow.workspace = true
+image.workspace = true
+tempfile.workspace = true

enkou-shaders/examples/gasket.rs

@@ -0,0 +1,85 @@
+use anyhow::{Context, Result};
+use enkou_shaders::Coefficients2;
+use enkou_shaders::camera::Camera;
+use enkou_shaders::chaos_game::ChaosGame;
+use enkou_shaders::image::{BlendMode, ImageSettings};
+use enkou_shaders::transform::Transform;
+use enkou_shaders::variation::Variation;
+use glam::{Affine2, UVec2, Vec2, uvec2, vec2};
+use image::{GrayImage, Luma};
+use rand::SeedableRng;
+use rand_xoshiro::Xoshiro256StarStar;
+use std::mem;
+use std::process::Command;
+use tempfile::NamedTempFile;
+
+const ITERATIONS_DISCARD: usize = 20;
+const ITERATIONS: usize = 50_000;
+const IMAGE_DIMENSION: UVec2 = uvec2(600, 600);
+
+pub fn main() -> Result<()> {
+    let mut rng = Xoshiro256StarStar::from_seed([4u8; 32]);
+
+    let transforms = [
+        {
+            // F_0: (x / 2, y / 2)
+            let coefficients = Affine2::from_coefficients(0.5, 0.0, 0.0, 0.0, 0.5, 0.0);
+            Transform::new(coefficients, Affine2::IDENTITY, uvec2(0, 1), vec2(0.0, 1.0))
+        },
+        {
+            // F_1: ((x + 1) / 2, y / 2)
+            let coefficients = Affine2::from_coefficients(0.5, 0.0, 0.5, 0.0, 0.5, 0.0);
+            Transform::new(coefficients, Affine2::IDENTITY, uvec2(0, 1), vec2(0.0, 1.0))
+        },
+        {
+            // F_2: (x / 2, (y + 1) / 2)
+            let coefficients = Affine2::from_coefficients(0.5, 0.0, 0.0, 0.0, 0.5, 0.5);
+            Transform::new(coefficients, Affine2::IDENTITY, uvec2(0, 1), vec2(0.0, 1.0))
+        },
+    ];
+
+    let weights = [1.0 / 3.0, 1.0 / 3.0, 1.0 / 3.0];
+
+    let variations = [Variation::IDENTITY];
+
+    // The gasket is defined on the range [0, 1] for both X and Y
+    let camera = Camera::new(
+        IMAGE_DIMENSION,
+        Vec2::ONE * 0.5,
+        0.0,
+        Vec2::ZERO,
+        IMAGE_DIMENSION.as_vec2(),
+    );
+
+    let image_settings = ImageSettings::new(BlendMode::Linear, IMAGE_DIMENSION);
+
+    let mut image = GrayImage::new(IMAGE_DIMENSION.x, IMAGE_DIMENSION.y);
+
+    let chaos_game = ChaosGame::new(&mut rng, &transforms, &weights, &variations);
+
+    chaos_game
+        .skip(ITERATIONS_DISCARD)
+        .take(ITERATIONS)
+        .map(|(point_ifs, _)| camera.transform_point(point_ifs))
+        .filter_map(|point_pixel| image_settings.transform_point_to_image(point_pixel))
+        .for_each(|point_pixel| image.put_pixel(point_pixel.x, point_pixel.y, Luma([255])));
+
+    let temp = NamedTempFile::with_suffix(".png").context("Unable to create file for image")?;
+    image.save(temp.path()).context("Unable to save image")?;
+
+    let open_program: &str = cfg_select! {
+        unix => "xdg-open",
+        _ => panic!("No available program to open images")
+    };
+
+    Command::new(open_program)
+        .arg(temp.path())
+        .spawn()?
+        .wait()?;
+
+    // In case the image viewer forks and gives control back prior to reading the file,
+    // drop it and don't run the destructor
+    mem::forget(temp);
+
+    Ok(())
+}

enkou-shaders/src/camera.rs

@@ -0,0 +1,164 @@
+//! # Camera
+//!
+//! Map points from the IFS coordinate system to pixel coordinates. This is a lossy transformation.
+use bytemuck::{Pod, Zeroable};
+use glam::{Affine2, IVec2, UVec2, Vec2, vec2};
+use libm::powf;
+
+/// Settings used to map IFS coordinates to pixel coordinates.
+///
+/// The camera is itself an affine transformation, capable of zoom, rotation, and translation
+/// of the IFS coordinates before rendering to the final image.
+#[derive(Copy, Clone, Pod, Zeroable)]
+#[repr(C)]
+pub struct Camera {
+    transform: Affine2,
+}
+
+impl Camera {
+    /// Construct a new camera for translating IFS coordinates to pixel coordinates.
+    ///
+    /// While the camera is implemented as a single affine transformation, it's helpful
+    /// to express the transform steps individually.
+    ///
+    /// # Arguments
+    /// * `blend_mode` - Color blending mode for the output image
+    /// * `dimensions` - Width and height of the output image (in pixels).
+    /// * `center` - Location of the origin in IFS coordinates. Positive `x` shifts the image
+    ///   left, and positive `y` position shifts the image up.
+    /// * `rotate` - Rotation angle (in radians) of IFS coordinates. Rotation is applied after the
+    ///   `center` translation, so it is about the new origin.
+    /// * `zoom` - Zoom factor applied to IFS coordinates. IFS coordinates are scaled by
+    ///   `pow(2, zoom)`, so a zoom factor of 0 is the identity.
+    /// * `scale` - Pixels per unit of IFS coordinates. This parameter is usually chosen such
+    ///   that the largest dimension will cover the range `[-2, 2]`, but values higher or lower
+    ///   can be used as a secondary zoom.
+    pub fn new(dimensions: UVec2, center: Vec2, rotate: f32, zoom: Vec2, scale: Vec2) -> Camera {
+        let ifs_center_transform = Affine2::from_translation(-center);
+        let zoom_transform = Affine2::from_scale(vec2(powf(2.0, zoom.x), powf(2.0, zoom.y)));
+        let scale_transform = Affine2::from_scale(scale);
+        let rotate_transform = Affine2::from_angle(rotate);
+        let image_center_transform = Affine2::from_translation((dimensions / 2).as_vec2());
+
+        let transform = image_center_transform
+            * rotate_transform
+            * scale_transform
+            * zoom_transform
+            * ifs_center_transform;
+
+        Camera { transform }
+    }
+
+    /// Map a point from IFS coordinates to pixel coordinates.
+    ///
+    /// ```
+    /// # use glam::{vec2, ivec2, uvec2, Vec2};
+    /// # use crate::enkou_shaders::camera::Camera;
+    /// // Output image is 600x600 pixels, centered at the origin, no rotation, no zoom,
+    /// // and scaled such that it covers the range [-2, 2].
+    /// // Use the origin as the IFS coordinate, so the pixel coordinate is the center of the image
+    /// let camera = Camera::new(
+    ///     uvec2(600, 600),
+    ///     Vec2::ZERO,
+    ///     0.0,
+    ///     Vec2::ZERO,
+    ///     vec2(150.0, 150.0)
+    /// );
+    /// assert_eq!(camera.transform_point(vec2(0.0, 0.0)), ivec2(300, 300));
+    /// ```
+    pub fn transform_point(&self, point: Vec2) -> IVec2 {
+        self.transform.transform_point2(point).as_ivec2()
+    }
+}
+
+#[cfg(test)]
+mod test {
+    use crate::camera::Camera;
+    use glam::{Affine2, Vec2, ivec2, uvec2, vec2};
+    use libm::powf;
+
+    #[test]
+    fn manual_camera() {
+        let starting_point = vec2(1.0, 1.0);
+
+        // Move the origin; points move right and up by one unit, giving us (2.0, 2.0)
+        let center = vec2(-1.0, -1.0);
+        let point = starting_point - center;
+
+        // Rotate about the new origin; points move counter-clockwise, giving us (-2.0, 2.0)
+        let rotate = 90.0f32.to_radians();
+        let point = Affine2::from_angle(rotate).transform_point2(point);
+
+        // Zoom in by a factor of 1; points will be twice as far from the origin,
+        // giving us (-4.0, 4.0)
+        let zoom = vec2(1.0, 1.0);
+        let point = point * vec2(powf(2.0, zoom.x), powf(2.0, zoom.y));
+
+        // Apply scaling; scale 100 in a 1000 x 1000 image is an effective range
+        // of [-5, 5] in IFS coordinates.
+        // After scaling, the point is (-400.0, 400.0)
+        let scale = vec2(100.0, 100.0);
+        let point = point * scale;
+
+        // Move the origin from (0, 0) to image center,
+        // giving us (100.0, 900.0)
+        let dimensions = uvec2(1000, 1000);
+        let point = point.as_ivec2() + dimensions.as_ivec2() / 2;
+
+        // Check that the camera implementation ends up at the same point
+        let camera = Camera::new(dimensions, center, rotate, zoom, scale);
+
+        // The camera is implemented by composing affine transforms,
+        // which ends up with a slightly different result because of rounding.
+        let error = (camera.transform_point(starting_point) - point)
+            .abs()
+            .as_uvec2();
+        assert!(error.x <= 1 && error.y <= 1);
+    }
+
+    #[test]
+    fn point_outside_camera() {
+        // Scale 250 for an image 1000 x 1000 gives an effective range of [-2, 2]
+        let camera = Camera::new(
+            uvec2(1000, 1000),
+            Vec2::ZERO,
+            0.0,
+            Vec2::ZERO,
+            vec2(250.0, 250.0),
+        );
+
+        // Converting a point outside the effective range is legal, but outside the image bounds
+        assert_eq!(camera.transform_point(vec2(3.0, 3.0)), ivec2(1250, 1250));
+    }
+
+    #[test]
+    fn point_outside_camera_negative() {
+        // Scale 250 for an image 1000 x 1000 gives an effective range of [-2, 2]
+        let camera = Camera::new(
+            uvec2(1000, 1000),
+            Vec2::ZERO,
+            0.0,
+            Vec2::ZERO,
+            vec2(250.0, 250.0),
+        );
+
+        // Converting a point outside the effective range is legal, but outside the image bounds
+        assert_eq!(camera.transform_point(vec2(-3.0, -3.0)), ivec2(-250, -250));
+    }
+
+    #[test]
+    fn aspect_ratio() {
+        // Scale 100 for an image 1600 x 900 gives an effective X range of [-8, 8],
+        // and effective Y range of [-4.5, 4.5]
+        let camera = Camera::new(
+            uvec2(1600, 900),
+            Vec2::ZERO,
+            0.0,
+            Vec2::ZERO,
+            vec2(100.0, 100.0),
+        );
+
+        // This point is inside the image width, but outside its height
+        assert_eq!(camera.transform_point(vec2(6.0, 6.0)), ivec2(1400, 1050));
+    }
+}

enkou-shaders/src/chaos_game.rs

@@ -0,0 +1,116 @@
+//! # Chaos Game
+//!
+//! Fractal flames are a class of
+//! [iterated function systems](https://en.wikipedia.org/wiki/Iterated_function_system)
+//! that generate images following a simple algorithm:
+//!
+//! - Pick a starting point `(x, y)`
+//! - Iterate:
+//!     - Pick a [`Transform`] from the set of available transforms
+//!     - Apply the current point to the chosen transform, generating a new point `(x, y)`
+//!     - Plot the new point `(x, y)`
+//!
+//! This algorithm is also known as the ["chaos game"](https://en.wikipedia.org/wiki/Chaos_game),
+//! and it forms the basic system for producing images.
+use crate::transform::Transform;
+use crate::variation::Variation;
+use rand::distr::{Distribution, StandardUniform};
+use rand::{Rng, RngExt};
+use spirv_std::glam::{Vec2, vec2};
+
+struct BiUnit;
+impl Distribution<f32> for BiUnit {
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f32 {
+        rng.sample::<f32, _>(StandardUniform) * 2.0 - 1.0
+    }
+}
+
+/// Iterate one step in the chaos game; choose the next transform, apply it,
+/// and return the resulting point. Also returns the transform index so that
+/// path-dependent weights (the "Xaos" table in Apophysis) can be chosen
+/// for the next iteration step.
+///
+/// # Arguments
+///
+/// * `weights` - Weights are assumed to be normalized; adding all elements together should return the value 1
+pub fn step_chaos_game<R: Rng>(
+    point: Vec2,
+    color: f32,
+    rng: &mut R,
+    transforms: &[Transform],
+    weights: &[f32],
+    variations: &[Variation],
+) -> (Vec2, f32, u32) {
+    let mut choice_weight = rng.sample::<f32, _>(StandardUniform);
+    let mut transform_index: u32 = 0;
+
+    for i in 0..weights.len() {
+        choice_weight -= weights[i];
+        if choice_weight <= 0.0 {
+            break;
+        }
+
+        transform_index += 1;
+    }
+
+    let transform = transforms[transform_index as usize];
+
+    (
+        transform.transform_point(rng, variations, point),
+        transform.transform_color(color),
+        transform_index,
+    )
+}
+
+/// Iterator for chaos game state. Holds the current point and references to all other data
+/// necessary to generate fractal flame images.
+///
+/// New points in the chaos game are produced by iterating on the chaos game.
+pub struct ChaosGame<'a, R: Rng> {
+    current_point: Vec2,
+    current_color: f32,
+    rng: &'a mut R,
+    transforms: &'a [Transform],
+    weights: &'a [f32],
+    variations: &'a [Variation],
+}
+
+impl<'a, R: Rng> ChaosGame<'a, R> {
+    /// Create a new chaos game iterator
+    pub fn new(
+        rng: &'a mut R,
+        transforms: &'a [Transform],
+        weights: &'a [f32],
+        variations: &'a [Variation],
+    ) -> Self {
+        let current_point = vec2(rng.sample(BiUnit), rng.sample(BiUnit));
+        let current_color = rng.sample(StandardUniform);
+        ChaosGame {
+            current_point,
+            current_color,
+            rng,
+            transforms,
+            weights,
+            variations,
+        }
+    }
+}
+
+impl<'a, R: Rng> Iterator for ChaosGame<'a, R> {
+    type Item = (Vec2, f32);
+
+    fn next(&mut self) -> Option<Self::Item> {
+        let (next_point, next_color, _) = step_chaos_game(
+            self.current_point,
+            self.current_color,
+            self.rng,
+            self.transforms,
+            self.weights,
+            self.variations,
+        );
+        self.current_point = next_point;
+        self.current_color = next_color;
+
+        Some((next_point, next_color))
+    }
+}

enkou-shaders/src/entry/image_accumulate.rs

@@ -0,0 +1,63 @@
+//! Image Accumulate
+
+use crate::camera::Camera;
+use crate::chaos_game::ChaosGame;
+use crate::image::ImageSettings;
+use crate::rng::xoshiro256starstar_from_seed;
+use crate::transform::Transform;
+use crate::variation::Variation;
+use glam::{UVec2, Vec4};
+use spirv_std::spirv;
+
+/// Run the chaos game and accumulate points into the output image buffer
+///
+/// # Arguments
+/// * `iterations` - Controls the iteration count; the first `x` iterations are discarded,
+///   the next `y` iterations are accumulated into the output image
+/// * `rng_seed`
+/// * `transforms`
+/// * `weights`
+/// * `variations`
+/// * `camera` - Camera transformation to map IFS coordinates to pixel coordinates
+/// * `image_settings` - Settings to use for image accumulation
+/// * `palette` - List of colors to use for the image palette; assumed to be RGB values scaled to `[0-255]`, with an alpha of 255
+/// * `image` - Output image buffer
+#[spirv(compute(entry_point_name = "main_image_accumulate", threads(1)))]
+pub fn main_image_accumulate(
+    #[spirv(storage_buffer, descriptor_set = 0, binding = 0)] iterations: &UVec2,
+    #[spirv(storage_buffer, descriptor_set = 0, binding = 1)] rng_seed: &[u8],
+    #[spirv(storage_buffer, descriptor_set = 0, binding = 2)] transforms: &[Transform],
+    #[spirv(storage_buffer, descriptor_set = 0, binding = 3)] weights: &[f32],
+    #[spirv(storage_buffer, descriptor_set = 0, binding = 4)] variations: &[Variation],
+    #[spirv(storage_buffer, descriptor_set = 0, binding = 5)] camera: &Camera,
+    #[spirv(storage_buffer, descriptor_set = 0, binding = 6)] image_settings: &ImageSettings,
+    #[spirv(storage_buffer, descriptor_set = 0, binding = 7)] palette: &[Vec4],
+    #[spirv(storage_buffer, descriptor_set = 1, binding = 0)] image: &mut [Vec4],
+) {
+    let mut rng_seed_actual = [0u8; 32];
+    for i in 0..rng_seed_actual.len() {
+        rng_seed_actual[i] = rng_seed[i];
+    }
+
+    let mut rng = xoshiro256starstar_from_seed(rng_seed_actual);
+
+    let chaos_game = ChaosGame::new(&mut rng, transforms, weights, variations);
+    let (iterations_fuse, iterations_accumulate) = (iterations.x, iterations.y);
+
+    let ifs_to_image = |(ifs_point, ifs_color)| {
+        let pixel_coordinates = camera.transform_point(ifs_point);
+        let pixel_color = image_settings.transform_color(ifs_color, palette);
+        image_settings
+            .transform_point_to_index(pixel_coordinates)
+            .map(|pixel_index| (pixel_index, pixel_color))
+    };
+
+    for ifs_point in chaos_game
+        .skip(iterations_fuse as usize)
+        .take(iterations_accumulate as usize)
+    {
+        if let Some((pixel_index, pixel_color)) = ifs_to_image(ifs_point) {
+            image[pixel_index as usize] = pixel_color;
+        }
+    }
+}

enkou-shaders/src/entry/mod.rs

@@ -0,0 +1,4 @@
+//! # Entry
+//!
+//! Entry points for Enkou shaders
+pub mod image_accumulate;

enkou-shaders/src/image.rs

@@ -0,0 +1,155 @@
+//! Image
+
+use bytemuck::{Pod, Zeroable};
+use glam::{IVec2, UVec2, Vec4};
+use libm::floorf;
+
+/// Blending modes for mapping IFS color values (which are on a scale `[0, 1]`)
+/// to RGBA colors.
+#[derive(Copy, Clone, Default)]
+#[repr(u32)]
+pub enum BlendMode {
+    /// Map IFS color values to a linear blend of the nearest two palette colors
+    #[default]
+    Linear = 0,
+
+    /// Map IFS color values to the nearest single palette color
+    Step = 1,
+}
+
+impl BlendMode {
+    /// Map an IFS color value to RGBA color from the provided palette.
+    pub fn ifs_to_rgb(&self, color: f32, palette: &[Vec4]) -> Vec4 {
+        let colors_m_one = palette.len() - 1;
+        let period = 1.0 / colors_m_one as f32;
+        let index_lower = floorf(color / period) as usize;
+        let index_upper = (index_lower + 1).clamp(0, colors_m_one);
+        let rem = color % period / period;
+
+        match self {
+            BlendMode::Linear => palette[index_lower].lerp(palette[index_upper], rem),
+            BlendMode::Step => palette[index_lower],
+        }
+    }
+}
+
+// UNSAFE: Sound because enum has guaranteed layout (u32) and defined zero-value
+unsafe impl bytemuck::Zeroable for BlendMode {}
+// UNSAFE: Sound because enum has guaranteed layout (u32) and defined zero-value
+unsafe impl bytemuck::Pod for BlendMode {}
+
+/// Settings to use for mapping the IFS coordinates to an output image
+#[derive(Copy, Clone, Pod, Zeroable)]
+#[repr(C)]
+pub struct ImageSettings {
+    blend_mode: BlendMode,
+    dimensions: UVec2,
+}
+
+impl ImageSettings {
+    /// Create a new settings object
+    pub fn new(blend_mode: BlendMode, dimensions: UVec2) -> Self {
+        ImageSettings {
+            blend_mode,
+            dimensions,
+        }
+    }
+
+    /// Map a point from camera coordinates to pixel coordinates,
+    /// and check that the result is within the provided image dimensions.
+    pub fn transform_point_to_image(&self, point: IVec2) -> Option<UVec2> {
+        if 0 <= point.x
+            && (point.x as u32) < self.dimensions.x
+            && 0 <= point.y
+            && (point.y as u32) < self.dimensions.y
+        {
+            Some(point.as_uvec2())
+        } else {
+            None
+        }
+    }
+
+    /// Map a point from camera coordinates to a final pixel index
+    pub fn transform_point_to_index(&self, point: IVec2) -> Option<u32> {
+        self.transform_point_to_image(point)
+            .map(|pixel| self.dimensions.with_x(1).dot(pixel))
+    }
+
+    /// Map an IFS color coordinate to the palette RGB value
+    pub fn transform_color(&self, color: f32, palette: &[Vec4]) -> Vec4 {
+        self.blend_mode.ifs_to_rgb(color, palette)
+    }
+}
+
+#[cfg(test)]
+mod test {
+    use crate::image::{BlendMode, ImageSettings};
+    use glam::{Vec4, ivec2, uvec2};
+
+    #[test]
+    fn blend_linear() {
+        let ifs_to_rgb = |color, palette| BlendMode::Linear.ifs_to_rgb(color, palette);
+
+        let palette = &[Vec4::splat(0.0), Vec4::splat(1.0)];
+        assert_eq!(ifs_to_rgb(0.0, palette), Vec4::splat(0.0));
+        assert_eq!(ifs_to_rgb(0.5, palette), Vec4::splat(0.5));
+        assert_eq!(ifs_to_rgb(1.0, palette), Vec4::splat(1.0));
+
+        let palette = &[Vec4::splat(1.0), Vec4::splat(2.0), Vec4::splat(3.0)];
+        assert_eq!(ifs_to_rgb(0.0, palette), Vec4::splat(1.0));
+        assert_eq!(ifs_to_rgb(0.5, palette), Vec4::splat(2.0));
+        assert_eq!(ifs_to_rgb(1.0, palette), Vec4::splat(3.0));
+
+        let palette = &[
+            Vec4::splat(1.0),
+            Vec4::splat(2.0),
+            Vec4::splat(3.0),
+            Vec4::splat(4.0),
+        ];
+        assert_eq!(ifs_to_rgb(0.0, palette), Vec4::splat(1.0));
+        assert_eq!(ifs_to_rgb(0.5, palette), Vec4::splat(2.5));
+        assert_eq!(ifs_to_rgb(1.0, palette), Vec4::splat(4.0));
+    }
+
+    #[test]
+    fn blend_step() {
+        let ifs_to_rgb = |color, palette| BlendMode::Step.ifs_to_rgb(color, palette);
+
+        let palette = &[Vec4::splat(0.0), Vec4::splat(1.0)];
+        assert_eq!(ifs_to_rgb(0.5, palette), Vec4::splat(0.0));
+
+        let palette = &[Vec4::splat(1.0), Vec4::splat(2.0), Vec4::splat(3.0)];
+        assert_eq!(ifs_to_rgb(0.0, palette), palette[0]);
+        assert_eq!(ifs_to_rgb(0.25, palette), palette[0]);
+        assert_eq!(ifs_to_rgb(0.4, palette), palette[0]);
+        assert_eq!(ifs_to_rgb(0.5, palette), palette[1]);
+        assert_eq!(ifs_to_rgb(0.7, palette), palette[1]);
+        assert_eq!(ifs_to_rgb(1.0, palette), palette[2]);
+    }
+
+    #[test]
+    fn image_bounds() {
+        let image_settings = ImageSettings::new(BlendMode::Linear, uvec2(100, 100));
+
+        assert!(
+            image_settings
+                .transform_point_to_image(ivec2(-1, -1))
+                .is_none()
+        );
+        assert!(
+            image_settings
+                .transform_point_to_image(ivec2(0, 0))
+                .is_some()
+        );
+        assert!(
+            image_settings
+                .transform_point_to_image(ivec2(99, 99))
+                .is_some()
+        );
+        assert!(
+            image_settings
+                .transform_point_to_image(ivec2(100, 100))
+                .is_none()
+        );
+    }
+}

enkou-shaders/src/lib.rs

@@ -1,36 +1,116 @@
+//! # Enkou
 #![no_std]
+#![warn(missing_docs)]
+// SPIR-V backend has issues with iteration over items:
+#![allow(clippy::needless_range_loop)]
+#![allow(clippy::manual_memcpy)]
+// Shader entry points are expected to have a lot of arguments:
+#![allow(clippy::too_many_arguments)]
 
-use bytemuck::{Pod, Zeroable};
-use core::f32::consts::PI;
-use glam::{Vec3, Vec4, vec2, vec3};
-#[cfg(target_arch = "spirv")]
-use spirv_std::num_traits::Float;
-use spirv_std::spirv;
+pub mod camera;
+pub mod chaos_game;
+pub mod entry;
+pub mod image;
+mod rng;
+pub mod transform;
+pub mod variation;
 
-#[derive(Copy, Clone, Pod, Zeroable)]
-#[repr(C)]
-pub struct ShaderConstants {
-    pub width: u32,
-    pub height: u32,
-    pub time: f32,
+use glam::Affine2;
+
+/// Utility trait to convert between `flam3` notation and [`glam`].
+#[allow(missing_docs)]
+pub trait Coefficients2 {
+    /// Convert affine transformation coefficients to the [`glam`] representation.
+    /// Parameters use the following form:
+    ///
+    /// ```text
+    /// (a * x + b * y + c, d * x + e * y + f)
+    /// ```
+    ///
+    /// ```
+    /// # use glam::{Affine2, vec2};
+    /// # use crate::enkou_shaders::Coefficients2;
+    /// let coefs = Affine2::from_coefficients(1.0, 2.0, 3.0, 4.0, 5.0, 6.0);
+    /// let (x, y) = (7.0, 8.0);
+    /// assert_eq!(
+    ///     coefs.transform_point2(vec2(x, y)),
+    ///     vec2(
+    ///         coefs.a() * x + coefs.b() * y + coefs.c(),
+    ///         coefs.d() * x + coefs.e() * y + coefs.f()
+    ///     )
+    /// );
+    /// ```
+    fn from_coefficients(a: f32, b: f32, c: f32, d: f32, e: f32, f: f32) -> Affine2;
+
+    /// Convert affine transformation coefficients to the [`glam`] representation.
+    /// Parameters use the following form:
+    ///
+    /// ```text
+    /// (a * x + b * y + c, d * x + e * y + f)
+    /// ```
+    ///
+    /// ```
+    /// # use glam::{Affine2, vec2};
+    /// # use crate::enkou_shaders::Coefficients2;
+    /// let coefs = Affine2::from_coefficients_arr([1.0, 2.0, 3.0, 4.0, 5.0, 6.0]);
+    /// let (x, y) = (7.0, 8.0);
+    /// assert_eq!(
+    ///     coefs.transform_point2(vec2(x, y)),
+    ///     vec2(
+    ///         coefs.a() * x + coefs.b() * y + coefs.c(),
+    ///         coefs.d() * x + coefs.e() * y + coefs.f()
+    ///     )
+    /// );
+    /// ```
+    fn from_coefficients_arr(coefficients: [f32; 6]) -> Affine2;
+
+    fn a(&self) -> f32;
+    fn b(&self) -> f32;
+    fn c(&self) -> f32;
+    fn d(&self) -> f32;
+    fn e(&self) -> f32;
+    fn f(&self) -> f32;
 }
 
-#[spirv(fragment)]
-pub fn main_fs(vtx_color: Vec3, output: &mut Vec4) {
-    *output = Vec4::from((vtx_color, 1.));
+impl Coefficients2 for Affine2 {
+    #[inline]
+    fn from_coefficients(a: f32, b: f32, c: f32, d: f32, e: f32, f: f32) -> Affine2 {
+        Affine2::from_cols_array(&[a, d, b, e, c, f])
     }
 
-#[spirv(vertex)]
-pub fn main_vs(
-    #[spirv(vertex_index)] vert_id: i32,
-    #[spirv(descriptor_set = 0, binding = 0, storage_buffer)] constants: &ShaderConstants,
-    #[spirv(position)] vtx_pos: &mut Vec4,
-    vtx_color: &mut Vec3,
-) {
-    let speed = 0.4;
-    let time = constants.time * speed + vert_id as f32 * (2. * PI * 120. / 360.);
-    let position = vec2(f32::sin(time), f32::cos(time));
-    *vtx_pos = Vec4::from((position, 0.0, 1.0));
-
-    *vtx_color = [vec3(1., 0., 0.), vec3(0., 1., 0.), vec3(0., 0., 1.)][vert_id as usize % 3];
+    #[inline]
+    fn from_coefficients_arr(coefficients: [f32; 6]) -> Affine2 {
+        Affine2::from_coefficients(
+            coefficients[0],
+            coefficients[1],
+            coefficients[2],
+            coefficients[3],
+            coefficients[4],
+            coefficients[5],
+        )
+    }
+
+    fn a(&self) -> f32 {
+        self.matrix2.x_axis.x
+    }
+
+    fn b(&self) -> f32 {
+        self.matrix2.y_axis.x
+    }
+
+    fn c(&self) -> f32 {
+        self.translation.x
+    }
+
+    fn d(&self) -> f32 {
+        self.matrix2.x_axis.y
+    }
+
+    fn e(&self) -> f32 {
+        self.matrix2.y_axis.y
+    }
+
+    fn f(&self) -> f32 {
+        self.translation.y
+    }
 }

enkou-shaders/src/rng.rs

@@ -0,0 +1,57 @@
+use rand::SeedableRng;
+use rand_xoshiro::Xoshiro256StarStar;
+
+/// Convert an RNG state buffer to an instance of [`Xoshiro256StarStar`].
+///
+/// While [`SeedableRng::from_seed`] is an infallible function,
+/// it relies on some methods that can't be compiled by the SPIR-V
+/// backend (specifically, formatting functions in the core crate).
+///
+/// In practice, the xoshiro RNG state is entirely defined by its seed,
+/// so this function does the work of [`SeedableRng::from_seed`] by
+/// transmuting the seed value to an RNG instance.
+///
+/// This function assumes a properly-initialized state array;
+/// output may silently degenerate if the initial state is all zeros,
+/// so this module is private to the crate.
+// Temporarily unused, will be required once the main image accumulation entry point is implemented
+#[allow(unused)]
+pub(crate) fn xoshiro256starstar_from_seed(
+    rng_state: <Xoshiro256StarStar as SeedableRng>::Seed,
+) -> Xoshiro256StarStar {
+    let mut rng_state_actual = [0u64; 4];
+
+    // NOTE: Bit shifting is bad, but we don't have great alternatives:
+    //  - `chunks_exact` has issues with pointer casting
+    //  - `u64::from_le_bytes` has issues with `OpBitcast` in SPIR-V validation
+    for i in 0..rng_state_actual.len() {
+        for j in 0..size_of::<u64>() {
+            rng_state_actual[i] |= (rng_state[i * size_of::<u64>() + j] as u64) << (j * 8);
+        }
+    }
+
+    unsafe { core::mem::transmute(rng_state_actual) }
+}
+
+#[cfg(test)]
+mod test {
+    use crate::rng::xoshiro256starstar_from_seed;
+    use core::iter::zip;
+    use rand::{RngExt, SeedableRng};
+    use rand_xoshiro::Xoshiro256StarStar;
+
+    #[test]
+    fn match_seeded() {
+        let mut seed: <Xoshiro256StarStar as SeedableRng>::Seed = [0u8; 32];
+        for i in 0..seed.len() {
+            seed[i] = i as u8;
+        }
+
+        let rng1 = Xoshiro256StarStar::from_seed(seed).random_iter::<u64>();
+        let rng2 = xoshiro256starstar_from_seed(seed).random_iter::<u64>();
+
+        zip(rng1, rng2)
+            .take(100)
+            .for_each(|(rng1_value, rng2_value)| assert_eq!(rng1_value, rng2_value));
+    }
+}

enkou-shaders/src/transform.rs

@@ -0,0 +1,135 @@
+//! # Transform
+//!
+//! Transforms are the "functions" in an iterated function system. They take in a point,
+//! and generate a new point. For fractal flames, transforms are always affine,
+//! but produce more interesting images once we add variations.
+use crate::variation::Variation;
+use bytemuck::{Pod, Zeroable};
+use glam::{Affine2, FloatExt, UVec2, Vec2};
+use rand::Rng;
+
+/// Affine transform for use in the [`chaos_game`](crate::chaos_game).
+#[derive(Copy, Clone, Pod, Zeroable)]
+#[repr(C)]
+pub struct Transform {
+    coefficients: Affine2,
+    coefficients_post: Affine2,
+    variation_range: UVec2,
+    color: Vec2,
+}
+
+impl Transform {
+    /// Create a new transform from an affine transformation matrix
+    pub fn new(
+        coefficients: Affine2,
+        coefficients_post: Affine2,
+        variation_range: UVec2,
+        color: Vec2,
+    ) -> Self {
+        Transform {
+            coefficients,
+            coefficients_post,
+            variation_range,
+            color,
+        }
+    }
+
+    /// Apply this transform to a point in IFS coordinates, producing a new point
+    pub fn transform_point<R: Rng>(
+        &self,
+        rng: &mut R,
+        variations: &[Variation],
+        point: Vec2,
+    ) -> Vec2 {
+        let point = self.coefficients.transform_point2(point);
+
+        let mut point_output = Vec2::ZERO;
+
+        let variation_start = self.variation_range.x;
+        let variation_end = self.variation_range.y;
+        for variation_index in variation_start..variation_end {
+            let variation = &variations[variation_index as usize];
+            point_output += variation.transform_point(point, rng, &self.coefficients)
+        }
+
+        self.coefficients_post.transform_point2(point)
+    }
+
+    /// Apply this transform to a color
+    pub fn transform_color(&self, color: f32) -> f32 {
+        color.lerp(self.color.x, self.color.y)
+    }
+}
+
+#[cfg(test)]
+mod test {
+    use crate::rng::xoshiro256starstar_from_seed;
+    use crate::transform::Transform;
+    use crate::variation::{Variation, VariationKind};
+    use glam::{Affine2, Vec2, uvec2, vec2};
+
+    #[test]
+    fn transform_scaling() {
+        let scale_coefficients = vec2(2.0, 0.5);
+        let transform = Transform::new(
+            Affine2::from_scale(scale_coefficients),
+            Affine2::IDENTITY,
+            uvec2(0, 1),
+            Vec2::ZERO,
+        );
+
+        let mut rng = xoshiro256starstar_from_seed([0; 32]);
+        let variations = [Variation::IDENTITY];
+        let point = vec2(1.0, 1.0);
+
+        assert_eq!(
+            transform.transform_point(&mut rng, &variations, point),
+            scale_coefficients
+        );
+    }
+
+    #[test]
+    fn transform_scaling_post() {
+        let scale_coefficients = vec2(2.0, 0.5);
+        let transform_pdj = Transform::new(
+            Affine2::IDENTITY,
+            Affine2::IDENTITY,
+            uvec2(0, 1),
+            Vec2::ZERO,
+        );
+        let transform_pdj_post = Transform::new(
+            Affine2::IDENTITY,
+            Affine2::from_scale(scale_coefficients),
+            uvec2(0, 1),
+            Vec2::ZERO,
+        );
+
+        let mut rng = xoshiro256starstar_from_seed([0; 32]);
+        let variations = [Variation::new(VariationKind::Pdj, 1.0, [0.0f32; 4].into())];
+        let point = vec2(1.0, 1.0);
+
+        let point_pdj = transform_pdj.transform_point(&mut rng, &variations, point);
+        let point_pdj_post = transform_pdj_post.transform_point(&mut rng, &variations, point);
+
+        assert_eq!(point_pdj * scale_coefficients, point_pdj_post);
+    }
+
+    #[test]
+    fn transform_color() {
+        // Color 0.5, color speed 1.0, so color value will always be 0.5 after transform
+        let color = vec2(0.5, 1.0);
+        let transform = Transform::new(Affine2::IDENTITY, Affine2::IDENTITY, uvec2(0, 1), color);
+
+        assert_eq!(transform.transform_color(0.0), 0.5);
+        assert_eq!(transform.transform_color(1.0), 0.5);
+        assert_eq!(transform.transform_color(2.0), 0.5);
+
+        // Color 1.0, color speed 0.5, so color value moves to halfway between current and 1.0
+        let color = vec2(1.0, 0.5);
+        let transform = Transform::new(Affine2::IDENTITY, Affine2::IDENTITY, uvec2(0, 1), color);
+
+        assert_eq!(transform.transform_color(0.0), 0.5);
+        assert_eq!(transform.transform_color(1.0), 1.0);
+        assert_eq!(transform.transform_color(2.0), 1.5);
+    }
+}

enkou-shaders/src/variation.rs

@@ -0,0 +1,132 @@
+//! # Variation
+//!
+//! Variations extend the fractal flame iterated function system
+//! with non-linear transforms (as opposed to [`Transform`]s,
+//! which are strictly affine transformations).
+use crate::Coefficients2;
+use bytemuck::{Pod, Zeroable};
+use core::f32::consts::PI;
+use glam::{Affine2, Vec2, vec2};
+use libm::{atan2f, cosf, powf, sinf, sqrtf, tanf};
+use rand::distr::StandardUniform;
+use rand::{Rng, RngExt};
+
+/// Generic variation parameters
+///
+/// Not all variations will use these parameters, but passing them
+/// as an array per variation allows shaders to use a consistent struct size
+/// no matter what the variation actually needs.
+#[derive(Copy, Clone, Pod, Zeroable)]
+#[repr(C)]
+pub struct VariationParams([f32; 4]);
+
+impl From<[f32; 4]> for VariationParams {
+    fn from(v: [f32; 4]) -> Self {
+        VariationParams(v)
+    }
+}
+
+/// Enum for all supported variation types
+///
+/// ID numbers are chosen to match the variation identifier also used by `flam3`
+#[derive(Copy, Clone)]
+#[repr(u32)]
+#[allow(missing_docs)]
+pub enum VariationKind {
+    /// Identity variation, returns the point as-is
+    Linear = 0,
+
+    Julia = 13,
+    Popcorn = 17,
+    Pdj = 24,
+}
+
+// UNSAFE: Sound because enum has guaranteed layout (u32) and defined zero-value
+unsafe impl bytemuck::Zeroable for VariationKind {}
+// UNSAFE: Sound because enum has guaranteed layout (u32) and defined zero-value
+unsafe impl bytemuck::Pod for VariationKind {}
+
+/// Parameters required for shaders to run the variation function.
+///
+/// Not all variations use the [`VariationParams`], but using the struct
+/// makes it easy to provide parameters to the shader.
+#[derive(Copy, Clone, Pod, Zeroable)]
+#[repr(C)]
+pub struct Variation {
+    kind: VariationKind,
+    weight: f32,
+    params: VariationParams,
+}
+
+impl Variation {
+    /// Identity variation; calling [`transform_point`] will yield
+    /// the same point as the input.
+    pub const IDENTITY: Variation = Variation {
+        kind: VariationKind::Linear,
+        weight: 1.0,
+        params: VariationParams([0f32; 4]),
+    };
+
+    /// Create a new variation by providing the variation kind, weight, and parameters.
+    pub fn new(kind: VariationKind, weight: f32, params: VariationParams) -> Variation {
+        Variation {
+            kind,
+            weight,
+            params,
+        }
+    }
+
+    /// Transform a point by applying this variation.
+    ///
+    /// Output points are scaled by this variation's weight.
+    pub fn transform_point<R: Rng>(
+        &self,
+        point: Vec2,
+        rng: &mut R,
+        coefficients: &Affine2,
+    ) -> Vec2 {
+        (match self.kind {
+            VariationKind::Linear => transform_point_linear(point),
+            VariationKind::Julia => transform_point_julia(point, rng),
+            VariationKind::Popcorn => transform_point_popcorn(point, coefficients),
+            VariationKind::Pdj => transform_point_pdj(point, &self.params),
+        }) * self.weight
+    }
+}
+
+fn transform_point_linear(point: Vec2) -> Vec2 {
+    point
+}
+
+fn transform_point_julia<R: Rng>(point: Vec2, rng: &mut R) -> Vec2 {
+    let x2 = powf(point.x, 2.0);
+    let y2 = powf(point.y, 2.0);
+    let r = sqrtf(x2 + y2);
+
+    let theta = atan2f(point.x, point.y);
+    let omega = if rng.sample::<f32, _>(StandardUniform) > 0.5 {
+        PI
+    } else {
+        0.0
+    };
+
+    let sqrt_r = sqrtf(r);
+    let theta_val = theta / 2.0 + omega;
+
+    vec2(sqrt_r * cosf(theta_val), sqrt_r * sinf(theta_val))
+}
+
+fn transform_point_popcorn(point: Vec2, coefficients: &Affine2) -> Vec2 {
+    vec2(
+        point.x * coefficients.c() * sinf(tanf(3.0 * point.y)),
+        point.y + coefficients.f() * sinf(tanf(3.0 * point.x)),
+    )
+}
+
+fn transform_point_pdj(point: Vec2, params: &VariationParams) -> Vec2 {
+    let (pdj_a, pdj_b, pdj_c, pdj_d) = (params.0[0], params.0[1], params.0[2], params.0[3]);
+    vec2(
+        sinf(pdj_a * point.y) - cosf(pdj_b * point.x),
+        sinf(pdj_c * point.x) - cosf(pdj_d * point.y),
+    )
+}